The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation. In recent years, this field has matured to a central area in Artificial Intelligence in general, and Knowledge Representation and Applied Logics in particular. This third volume of the Handbook is organised into three parts, containing thirteen chapters in all, each written by leading experts in the field. The first part contains surveys of applications of formal argumentation, such as in social network analysis, legal reasoning, general decision-making, and many more. The second part is about connections of the field of formal argumentation to other fields, such as logic programming, conditional reasoning, machine learning, and others. Finally, the third part provides some perspectives and future directions, in particular concerning current scientific challenges. The Handbook of Formal Argumentation is an open-ended initiative of which the present volume is the third outcome. Further volumes are planned to cover topics not included in the ones up this one and the initiative is conceived to grow by the support and feeding it receives from the community members.